Halliday, Resnick & Walker — Waves–I: Problem Problem_69

Three sinusoidal waves of the same frequency travel along a string in the positive direction of an \(x\) axis. Their amplitudes are \(y_1\), \(y_1/2\), and \(y_1/3\), and their phase constants are \(0, \pi/2\), and \(\pi\), respectively. What are the (a) amplitude and (b) phase constant of the resultant wave? (c) Plot the wave form of the resultant wave at \(t = 0\), and discuss its behavior as \(t\) increases.